CLEP College Mathematics
CLEP College
Mathematics
AT A GLANCE
Description of the Examination
CLEP?
The
College Mathematics examination covers
material generally taught in a college course for
nonmathematics majors and majors in fields not requiring
knowledge of advanced mathematics.
The exam contains 60 questions to be answered in
97 minutes. Some of these are pretest questions that won't
be scored. Any time candidates spend on tutorials and
providing personal information is in addition to the actual
testing time.
An online scientific (nongraphing) calculator will be available
during the exam. Although a calculator isn't necessary
to answer most of the questions, the solutions of a few
problems may be difficult to obtain without a calculator.
Because no calculator is allowed during the exam except for
the online calculator provided, it's recommended that prior
to the exam, you become familiar with the use of the online
calculator.
For more information about downloading the practice
version of the scientific (nongraphing) calculator, please visit
the College Mathematics description on the CLEP website:
clep.science-and-mathematics/
college-mathematics.
It's assumed that candidates are familiar with currently
taught mathematics vocabulary, symbols, and notation.
Knowledge and Skills Required
Questions on the College Mathematics exam require
candidates to demonstrate the following abilities in the
approximate proportions indicated.
¡ì Solving routine, straightforward problems (about 50%
of the exam)
¡ì Solving nonroutine problems requiring an
understanding of concepts and the application of skills
and concepts (about 50% of the exam)
The subject matter of the College Mathematics exam is
drawn from the following topics. The percentages next to
the main topics indicate the approximate percentage of
exam questions on each topic.
20% ALGEBRA AND FUNCTIONS
¡ì Solving equations, linear inequalities, and systems of
linear equations by analytic and graphical methods
¡ì Properties of triangles and quadrilaterals: perimeter,
area, similarity, and the Pythagorean theorem
¡ì Interpretation, representation, and evaluation of
functions: numerical, graphical, symbolic, and
descriptive methods
¡ì Parallel and perpendicular lines
¡ì Graphs of functions: translations, horizontal and vertical
reflections, and symmetry about the x-axis, the y-axis,
and the origin
¡ì Linear and exponential growth
¡ì Applications
¡ì Types of functions that will be considered are linear,
polynomial, radical, exponential, logarithmic, and
piecewise defined.
10% COUNTING AND PROBABILITY
¡ì Properties of circles: circumference, area, central
angles, inscribed angles, and sectors
¡ì Applications
15% LOGIC AND SETS
¡ì Logical operations and statements: conditional
statements, conjunctions, disjunctions, negations,
hypotheses, logical conclusions, converses, inverses,
counterexamples, contrapositives, and logical
equivalence
¡ì Set relationships, subsets, disjoint sets, equality of sets,
and Venn diagrams
¡ì Counting problems: the multiplication rule,
combinations, and permutations
¡ì Operations on sets: union, intersection, complement,
and Cartesian product
¡ì Probability: union, intersection, independent events,
mutually exclusive events, complementary events,
conditional probabilities, and expected value
¡ì Applications
¡ì Applications
15% DATA ANALYSIS AND STATISTICS
10% NUMBERS
¡ì Properties of numbers and their operations: integers
and rational, irrational, and real numbers (including
recognizing rational and irrational numbers)
¡ì Data interpretation and representation: tables,
bar graphs, line graphs, circle graphs, pie charts,
scatterplots, and histograms
¡ì Elementary number theory: factors and divisibility,
primes and composites, odd and even integers, and the
fundamental theorem of arithmetic
¡ì Numerical summaries of data: mean (average), median,
mode, and range
¡ì Measurement: unit conversion, scientific notation, and
numerical precision
¡ì Standard deviation and normal distribution (conceptual
questions only)
¡ì Absolute value
¡ì Applications
20% FINANCIAL MATHEMATICS
¡ì Percents, percent change, markups, discounts, taxes,
profit, and loss
¡ì Interest: simple, compound, continuous interest,
effective interest rate, and effective annual yield or
annual percentage rate (APR)
¡ì Present value and future value
¡ì Applications
2
10% GEOMETRY
¡ì Applications
Sample Test Questions
Study Resources
The following sample questions don't appear on an actual
CLEP exam. They're intended to give potential test takers
an indication of the format and difficulty level of the exam
and to provide content for practice and review. Knowing
the correct answers to all of the sample questions isn't a
guarantee of satisfactory performance on the exam.
Most textbooks used in college-level mathematics
courses cover the topics in the outline given earlier,
but the approaches to certain topics and the emphasis
given to them may differ. To prepare for the College
Mathematics exam, it's advisable to study one or more
introductory college-level mathematics textbooks,
which can be found in most college bookstores or
online. Elementary algebra textbooks also cover many
of the topics on the College Mathematics exam. When
selecting a textbook, check the table of contents against
the knowledge and skills required for the test. Visit
clep.earn-college-credit/practice for
additional math resources. You can also find suggestions for
exam preparation in Chapter IV of the CLEP Official Study
Guide. In addition, college faculty post their course materials
on their school¡¯s website.
Directions: An online scientific calculator will be available for
the questions in this test. Some questions will require you to
select from among four choices. For these questions, select
the BEST of the choices given. Some questions will require
you to type a numerical answer in the box provided. Some
questions will refer to a table in which statements appear
in the first column. For each statement, select the correct
properties by checking the appropriate cell(s) in the table.
Notes: (1) Unless otherwise specified, the domain of any
function f is assumed to be the set of all real
numbers x for which f (x) is a real number.
(2) Figures that accompany questions are intended
to provide information useful in answering the
questions. The figures are drawn as accurately
as possible EXCEPT when it's stated in a specific
question that the figure isn't drawn to scale.
Sample Questions
1.
(3) For a universal set U and X, a subset of U, the
complement of X, denoted as X C, is defined as
the set of elements of U that are not in X.
(4) Profit equals Revenue minus Cost.
(5) If a principal of P dollars is invested at an annual
interest rate r, compounded n times per year,
and no further withdrawals or deposits are made
to the account, then the future value A, the
account balance after t years, is given by
the formula A = P 1+
r
n
nt
(7) At an interest rate r, compounded n times
per year, the effective annual yield, or annual
percentage rate (APR), is given by the
formula APR = 1+
3
r
n
n
2
2.
1.
(4 ¡Á10?5 )
3
(2 ¡Á106 )
A.
B.
C.
D.
.
(6) If a principal of P dollars is invested at an annual
interest rate r and is compounded continuously,
and no further withdrawals or deposits are
made to the account, then the future value A,
the account balance after t years, is given by the
formula A = Pe rt.
Audrey deposited $10,000 into a 3-year certificate of
deposit that earned 10% annual interest, compounded
annually. Audrey made no additional deposits to or
withdrawals from the certificate of deposit. What was
the value of the certificate of deposit at the end of the
3-year period?
A. $13,000
B. $13,300
C. $13,310
D. $13,401
3.
=
2 x 10 ¨C2?
1.3 x 10 ¨C2
1.6 x 10 10
2 x 10 14
If P dollars is invested in a savings account that pays
5% annual interest, compounded continuously,
in how many years will the account value be equal to
2P dollars?
A. 20 ln(2) years
B. 5 ln(2) years
C. 10 years
D. 20 years
4.
Assume that a and b are positive integers. For each
statement below, determine whether the statement is true
or false, and indicate your answer in the appropriate box.
Statement
8.
6
11
B. 26
C. 38
D. 48
A.
True False
2
2
If a is divisible by b, then a is divisible by b .
2
If a is divisible by b, then a is divisible by b.
2
If a is divisible by b , then a is divisible by b.
5.
9.
From 1950 to 1990, the population of Country W
increased by 40%. From 1990 to 2012, the population of
Country W increased by 10%. What is the percent increase
in the population of Country W from 1950 to 2012?
%
6.
Let P(E) represent the probability of event E. Let A and B
be events with P(B) = 0.7, and P(A¡ÉB) = 0.2. What is the
value of P(A¡ÈB)?
A. 1.0
B. 0.9
C. 0.8
D. 0.7
Number of Teachers
600
500
400
300
200
100
40
A
500
2005
2010
375 400
300
0
7.
NUMBER OF TEACHERS IN FOUR CITIES,
2005 AND 2010
B
City
C
D
The chart above shows the number of teachers in City A,
City B, City C, and City D in 2005 and 2010. Which
city had the greatest percent increase in the number of
teachers from 2005 to 2010 ?
A. City A
B. City B
C. City C
D. City D
x ?2
, then f ( g (¨C4)) =
x +3
There are 220 seniors at a certain school. Among all
seniors at the school, 45 took calculus, 55 took physics,
and 10 took both. How many seniors took neither
calculus nor physics?
A. 90
B. 100
C. 120
D. 130
Airline/ Departure
Morning
Afternoon
Total
Airmoon flights
4
6
10
Airsun flights
7
8
15
Total
11
14
25
10. There are 10 Airmoon flights and 15 Airsun flights daily
from Yorktown to Newcity, as shown in the table above.
The table shows that 4 Airmoon and 7 Airsun flights
depart in the morning and the remaining flights depart
in the afternoon. If a flight is to be selected at random
from among the flights that depart in the afternoon
from Yorktown to Newcity, what is the probability that
the flight selected will be an Airmoon flight?
A.
100 115
100
If f (x) = x2 + x ¨C 4 and g(x) =
B.
C.
D.
6
25
6
14
10
25
14
25
11. In a sleep study, there are 50 people who are 20 years old,
50 people who are 25 years old, and 50 people who
are 30 years old. If an additional 20-year-old person
participates in the study, what happens to the average age,
the median age, and the age range of the participants in
the study?
Increases Decreases Does Not Change
Average age
Median age
Age range
Click on your choices.
4
Credit Recommendations
The American Council on Education has recommended
that colleges grant three credits for a score of 50, which is
equivalent to a course grade of C, on the CLEP College
Mathematics exam. Each college, however, is responsible
for setting its own policy. For candidates with satisfactory
scores on the College Mathematics exam, colleges may
grant credit toward fulfillment of a distribution requirement,
or for a particular course that matches the exam in content.
Check with your school to find out the score it requires for
granting credit, the number of credit hours granted, and the
course that can be bypassed with a passing score.
Answers to Sample Questions:
1-C; 2-A; 3-A; 4-see below; 5-54; 6-C; 7-B; 8-C; 9-D; 10-B;
11-see below
4.
Statement
True False
2
2
If a is divisible by b, then a is divisible by b .
?
2
?
If a is divisible by b, then a is divisible by b.
2
If a is divisible by b , then a is divisible by b.
?
11.
Increases
Average age
5
Decreases Does Not Change
?
Median age
?
Age range
?
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